A heavy nucleus Q of half-life 20 minutes undergoes alpha-decay with probability of 60 % and beta-decay with…

Given,

$T_{\frac{1}{2}}=20 \min$

$N_0=1000$

$\because 1 \mathrm{hour}=60 \min =3T_{\frac{1}{2}}$

$\therefore$ Number of nuclei remain after $1$ hour,

$N=\frac{N_o}{2^3}=\frac{1000}{8}$

$\Rightarrow N=125$

It means $875$ nuclei has decayed,

Now,

Number of $\alpha$ decayed Nucleus

$=\frac{875\times 60}{100}=525$